For this "resisting a push" problem, the best way I can think of to solve the problem is to create the smallest angle between the incoming force and the ground.
(click to enlarge)
Nice pictures, they very much illuminate what you mean by the atheletic approach to receiving a push, but I'm curious as to how would you draw these again for the person in the diagram where the angle of force that will be applied is not known in advance of its arrival?
(Maybe draw a blindfold on the man so he can't see?)
I'm interested to see! (I'm leaving my blindfold off...)